setLinearAlgebra

setLinearAlgebra - ARNOLD PIZER Rochester WeBWorK Problem...

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ARNOLD PIZER rochester problib from CVS July 7, 2004 Rochester WeBWorK Problem Library WeBWorK assignment LinearAlgebra1Systems due 1/1/09 at 2:00 AM 1. (1 pt) setLinearAlgebra1Systems/ur la 1 3.pg Solve the system using substitution x - 2 y = 1 4 x - 7 y = 5 x = y = 2. (1 pt) setLinearAlgebra1Systems/ur la 1 4.pg Solve the system using substitution - 4 x - 5 y = 54 7 x + 3 y = - 60 x = y = 3. (1 pt) setLinearAlgebra1Systems/ur la 1 4a.pg Solve the system using elimination - 2 x - 9 y = 42 - 5 x - 9 y = 24 x = y = 4. (1 pt) setLinearAlgebra1Systems/ur la 1 5.pg Solve the system using elimination 4 x + 3 y - 5 z = 14 3 x + 4 y + 6 z = - 1 6 x - 5 y - 6 z = 29 x = y = z = 5. (1 pt) setLinearAlgebra1Systems/ur la 1 23.pg Write the system - 6 y + 9 z = - 5 4 x - 4 y = 10 2 x + 11 y - 7 z = - 2 in matrix form. x y z = 6. (1 pt) setLinearAlgebra1Systems/ur la 1 7.pg Write the augmented matrix of the system - 73 y + 2 z = 9 8 x + 83 z = 2 5 x + 5 y - z = - 9 7. (1 pt) setLinearAlgebra1Systems/ur la 1 1.pg Perform one step of row reduction, in order to calculate the val- ues for x and y by back substitution. Then calculate the values for x and for y. Also calculate the determinant of the original matrix. You can let webwork do much of the calculation for you if you want (e.g. enter 45-(56/76)(-3) instead of calculating the value out). You can also use the preview feature in order to make sure that you have used the correct syntax in entering the answer. [Note– since the determinant is unchanged by row reduction it will be easier to calculate the determinant of the row reduced matrix.] 1 36 18 43 x y = -5 4 1 36 0 x y = -5 x = y = det = 8. (1 pt) setLinearAlgebra1Systems/ur la 1 2.pg Perform one step of row reduction, in order to calculate the val- ues for x and y by back substitution. Then calculate the values for x and for y. Also calculate the determinant of the original matrix. You can let webwork do much of the calculation for you if you want (e.g. enter 45-(56/76)(-3) instead of calculating the value out). You can also use the preview feature in order to make sure that you have used the correct syntax in entering the answer. This problem has rather difficult complex calculations. [Note– since the determinant is unchanged by row reduction it will be easier to calculate the determinant of the row reduced matrix.] 4-3i -4-5i 5 4-3i x y = -56-21i -12-41i 4-3i -4-5i 0 x y = -56-21i x = y = det = 9. (1 pt) setLinearAlgebra1Systems/ur la 1 4b.pg Solve the system using matrices (row operations) - 2 x + 9 y = 55 - 5 x - 9 y = - 83 x = y = 10. (1 pt) setLinearAlgebra1Systems/ur la 1 5a.pg Solve the system using matrices (row operations) - 2 x - 3 y + 5 z = 13 - 3 x - 6 y + 2 z = - 4 5 x - 3 y - 4 z = - 9 x = 1
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y = z = 11. (1 pt) setLinearAlgebra1Systems/ur la 1 16.pg Solve the system x + y = 12 3 x - 2 y = 21 10 x - 5 y = 75 x = y = 12. (1 pt) setLinearAlgebra1Systems/ur la 1 17.pg Solve the system x 1 + 3 x 3 + 4 x 4 = 33 x 2 - 3 x 3 - 2 x 4 = - 25 3 x 1 - 2 x 2 + 11 x 3 + 16 x 4 = 117 - x 2 + 3 x 3 + 6 x 4 = 37 x 1 = x 2 = x 3 = x 4 =
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